Nuprl Lemma : assert-is-rat-cube-face
∀k:ℕ. ∀c,d:ℚCube(k). uiff(↑is-rat-cube-face(k;c;d);c ≤ d)
Proof
Definitions occuring in Statement :
is-rat-cube-face: is-rat-cube-face(k;c;d),
rat-cube-face: c ≤ d,
rational-cube: ℚCube(k),
nat: ℕ,
assert: ↑b,
uiff: uiff(P;Q),
all: ∀x:A. B[x]
Definitions unfolded in proof :
prop: ℙ,
uall: ∀[x:A]. B[x],
not: ¬A,
false: False,
bfalse: ff,
true: True,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
btrue: tt,
ifthenelse: if b then t else f fi ,
assert: ↑b,
isl: isl(x),
or: P ∨ Q,
decidable: Dec(P),
implies: P ⇒ Q,
member: t ∈ T,
is-rat-cube-face: is-rat-cube-face(k;c;d),
all: ∀x:A. B[x]
Lemmas referenced :
istype-nat,
rational-cube_wf,
rat-cube-face_wf,
istype-void,
istype-true,
rat-cube-face-decider_wf
Rules used in proof :
equalityIstype,
isectElimination,
universeIsType,
independent_functionElimination,
voidElimination,
natural_numberEquality,
rename,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
isect_memberFormation_alt,
independent_pairFormation,
sqequalRule,
unionElimination,
inhabitedIsType,
hypothesis,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}k:\mBbbN{}. \mforall{}c,d:\mBbbQ{}Cube(k). uiff(\muparrow{}is-rat-cube-face(k;c;d);c \mleq{} d)
Date html generated:
2019_10_29-AM-07_50_22
Last ObjectModification:
2019_10_19-AM-10_50_12
Theory : rationals
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